Math 261 – Linear Algebra I – Fall 2025

This page contains some information that can be helpful before you register for the course. After registration, we will use ODTUclass. You should follow ODTUclass and check your emails regularly for important announcements during the semester.

Course Objectives

This course introduces the fundamental tools of linear algebra, offering both a rigorous theoretical framework and attention to computational methods. It emphasizes a detailed exploration of linear transformations and matrix theory, concepts that are central to the theoretical foundations and practical applications of linear algebra.

Lecture Hours

The lectures will be held in M13 during the following hours.

  • Tuesday 13:40-15:30
  • Thursday 13:40-15:30

Grading

There will be two midterms exams and a final exam.

  • Midterm 1, 30 points – TBA.
  • Midterm 2, 30 points – TBA.
  • Final Exam, 40 points – TBA by Student Affairs.

Textbook

  • Friedberg, Insel, Spence, Linear Algebra (4th edition).

Tentative Course Outline

The course content, together with a tentative course outline, can be found below. We will attempt to cover the related parts of the textbook each week.

  • Week 1: (Sep 29 – Oct 3) Introduction, Vector Spaces, Subspaces. 1-23.
  • Week 2: (Oct 6 – Oct 10) Linear Combinations and Linear Equations, Linear Dependence and Linear Independence. 24-41.
  • Week 3: (Oct 13 – Oct 17) Bases and Dimension. 42-57.
  • Week 4: (Oct 20 – Oct 24) Sums and Direct Sums, Quotient Spaces. 22, 23, 57, 58.
  • Week 5: (Oct 27 – Oct 31) Linear Transformations, Null Spaces and Ranges. 64-78.
  • Week 6: (Nov 3 – Nov 7) The Matrix Representation of a Linear Transformation, Composition of Linear Transformations and Matrix Multiplication. 79-98.
  • Week 7: (Nov 10 – Nov 14) Invertibility and Isomorphisms. 99-109.
  • Week 8: (Nov 17 – Nov 21) The Change of Coordinate Matrix, Dual Spaces. 110-126.
  • Week 9: (Nov 24 – Nov 28) Elementary Matrix Operations and Elementary Matrices, The Rank of a Matrix and Matrix Inverses. 147-167.
  • Week 10: (Dec 1 – Dec 5) Systems of Linear Equations – Theoretical Aspects. 168 -181.
  • Week 11: (Dec 8 – Dec 12) Systems of Linear Equations – Computational Aspects. 182-197.
  • Week 12: (Dec 15 – Dec 19) Determinants of Order 2, Determinants of Order n. 199-221.
  • Week 13: (Dec 22 – Dec 26) Properties of Determinants. 222-243.
  • Week 14: (Dec 29 – Jan 2) Some Examples.

Pari/GP

The software Pari/GP is very simple to learn and extremely strong to do computations with.

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